Page 124 - IJB-10-6

International Journal of Bioprinting Fluid mechanics of extrusion bioprinting

nitrogen) or a mechanical system with a piston or screw to form of an intended structure ; this is characterized by
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drive the liquid biomaterial. factors such as extrudability, filament fidelity, and structural
While pneumatic-driven systems are widely used in integrity. Printability depends on various parameters,
most commercial bioprinters because of their simplicity, including the viscosity and surface tension of the bioink,
they possess a main drawback caused by gas compressibility. the crosslinking time, as well as the surface properties of
36,39
As a result, pneumatic-driven systems lack accurate control the printing stage and printer nozzle. Table 1 presents
over the start and stop in extrusion or printing. This can the printability criteria, the factors characterizing them,
be offset by using a valve-based pneumatic system that and how they affect printing outcomes. Regarding the
facilitates high-precision extrusion by controlled pressure extrudability, there are four typical cases for the extrusion
and pulse frequency. 31,32 Additionally, the pneumatic- of bioinks (Figure 1): (i) unextrudable, (ii) discontinuous
driven system is not suitable for printing highly viscous (dripping), (iii) continuous but uncontrollable (with
bioinks, which requires high pressures and may lead to gobbling drop 52,53 ), and (iv) continuous and controllable
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related issues. 33 (jetting). These cases can be recognized by comparing the
effective forces on the flow of bioink. To successfully extrude
The piston- and screw-driven systems are more bioink from the nozzle, the inertial force (characterizing
accurate in extrusion or printing as the linear displacement the acceleration of the fluid) should dominate the capillary
of the piston or rotation of the screw can be accurately force from the surface tension of the bioink that tends to
controlled compared to the gas pressure in the pneumatic-
driven system. Moreover, both piston- and screw-driven keep it attached to the nozzle.
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systems are good for printing high-viscosity bioinks, The entire extrusion bioprinting process occurs within
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though it has been reported that the screw-driven system the laminar flow regime, characterized by low Reynolds
generally induces more cell damage compared to the number (Re). Reynolds number is a dimensionless
pneumatic-driven system. 36 quantity that compares inertial and viscous forces in the
flow. For the flow of a Newtonian fluid inside a needle, Re
2.2. Printability is defined as :
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During the extrusion bioprinting process, each layer
is stacked on top of the previous one to construct a 3D
scaffold. To ensure the stability of the printed construct, Re = ρUd (I)
the filaments need to solidify after being deposited on η
the printing stage. This solidification process is achieved
through a crosslinking process, which can be either physical where  and h represent the density and dynamic
or chemical. However, the time required for crosslinking viscosity of the fluid, respectively, d is the diameter of the
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-
can pose challenges. During gelation, the bioink (in liquid needle, and U the average velocity of the flow inside the
form) may flow and spread on the printing stage, causing needle. Due to the relatively high viscosity, the small size of
deformations and deviations from the intended geometry. the dispensing needle, and the slow velocity of the bioink
This deviation from the designed structure is characterized during the extrusion, extrusion bioprinting typically
by printability. In some cases, the flow of the deposited exhibits extremely low Re. This results in a special laminar
bioink can even lead to the collapse of the entire structure, flow regime known as creeping flow, characterized by the
rendering it unprintable. Printability significantly affects dominance of viscous forces, facilitating the smooth
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the mechanical and biological properties of the printed deposition of filaments. Another important parameter in
construct, such as its mechanical strength and cellular extrusion bioprinting is the Weber number, which is the
functionality. To evaluate printability, it is common ratio of inertial to capillary forces, presented as :
6–8
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to analyze the differences between the printed construct
and the intended design, considering factors such as 2
filament diameter and pore size. These evaluations can be We = ρURi (II)
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qualitative, relying on visual observations, or quantitative, ζ
involving the use of numerical indices. There are
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various definitions of printability in the literature, 38,39 where ρ is bioink density, R is the internal radius of
i
each considering printability from different perspectives the nozzle, and z denotes the surface tension of the bioink.
to explain the ability to print a 3D construct that closely For a given nozzle radius and bioink properties, the Weber
matches the one designed in computer-aided design number is determined by the flow rate, which depends on
(CAD) software. In this review, we adopt the definition of the dispensing force applied by the driving mechanism to
printability as the capability to create and uphold the 3D the bioink.

Volume 10 Issue 6 (2024) 116 doi: 10.36922/ijb.3973